Finite Group Databasebeta

← C2×#10624040 #13089023

Subgroups — C2×#10624040 #13089023

Order 1440.

678 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67158C211yesmaximal, characteristic, complemented
2C2×#67149C212yesmaximal
3C2×C5×#627C211yesmaximal, characteristic, complemented
4C2×#67137C211yesmaximal, characteristic
5C2×C3×#1204C212yesmaximal, complemented
6#10624040C218yesmaximal, direct product factor
7C2×D15⋊Q8—32nomaximal
8C22×C3⋊D15C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C3×Dic15C2212yes—
11C2×C3×C5×Dic3C2212yes—
12C2×C32×Dic5C2211yescharacteristic
13#67158C2214yescomplemented
14#67149C2218yes—
15C5×#627C2214yescomplemented
16#67137C2214yes—
17C3×#1204C2218yescomplemented
18C2×#3797—51nomaximal, Hall
19C2×C4×D15—32no—
20C2×C5×Dic6—32no—
21C2×C3×Dic10—32no—
22C2×#1204—32no—
23C2×#1204D312yescomplemented
24C2×#1200—32no—
25C2×#1200—32no—
26C2×#1200—61no—
27D15⋊Q8—316no—
28C22×C32×C5C2311yescharacteristic
29C2×C3⋊D15Q814yescomplemented
30C2×C3⋊D15C2312yes—
31C5×C3⋊Dic3C2312yes—
32C3×Dic15C2314yes—
33C3×C5×Dic3C2314yes—
34C32×Dic5C2312yes—
35C2×Q8×D5—91noHall
36C2×C4×C3⋊D3—51no—
37C2×C3×Dic6—52no—
38C2×#627—51no—
39C2×#627D511yescharacteristic, complemented
40C2×#624—52no—
41#3797—58no—
42C22×D15—32no—
43C22×D15—61no—
44C2×C3×C4×C5—32no—
45C2×Dic15C2×D312yes—
46C4×D15—38no—
47C2×C5×Dic3—32no—
48C2×C5×Dic3—61no—
49C2×C5×Dic3C2×D312yes—
50C5×Dic6—38no—
51C2×C3×Dic5—21no—
52C2×C3×Dic5—32no—
53C2×C3×Dic5C2×D312yes—
54C3×Dic10—38no—
55#1204—38no—
56#1204C2×D318yescomplemented
57#1200—38no—
58#1200—38no—
59#1200—64no—
60C2×D3×Q8—152no—
61C2×C32×C5C2×Q812yescomplemented
62C2×C32×C5C2411yescharacteristic
63C3⋊D15C2×Q814yescomplemented
64C2×C5×Q8—91no—
65Q8×D5—98no—
66C2×C4×D5—92no—
67C2×C4×D5—91no—
68C2×Dic10—32no—
69C2×Dic10—91no—
70C22×C3⋊D3—51no—
71C2×C32×C4—51no—
72C2×C3⋊Dic3C2×D511yescharacteristic
73C4×C3⋊D3—54no—
74C2×C3×Dic3—52no—
75C2×C3×Dic3C2×D512yes—
76C3×Dic6—58no—
77#627—54no—
78#627C2×D514yescomplemented
79#624—58no—
80C22×C3×C5—21no—
81C22×C3×C5C22×D312yes—
82C2×D15—38no—
83C2×D15—34no—
84C2×D15—64no—
85C2×D15—62no—
86C3×C4×C5—34no—
87Dic15C22×D314yes—
88C3×Dic5—22no—
89C3×Dic5—34no—
90C3×Dic5C22×D314yes—
91C5×Dic3—34no—
92C5×Dic3—62no—
93C5×Dic3C22×D314yes—
94C2×C3×Q8—152no—
95D3×Q8—1516no—
96C2×C4×D3—152no—
97C2×C4×D3—152no—
98C2×C4×D3—152no—
99C2×C4×D3—301no—
100C2×Dic6—32no—
101C2×Dic6—52no—
102C2×Dic6—152no—
103C32×C5C22×Q811yescharacteristic, complemented, Hall
104C22×D5—91no—
105C5×Q8—94no—
106C2×C4×C5—32no—
107C2×C4×C5—91no—
108C2×Dic5—32no—
109C2×Dic5D3211yescharacteristic
110C4×D5—98no—
111C4×D5—94no—
112Dic10—38no—
113Dic10—94no—
114C22×C32C22×D511yescharacteristic
115C2×C3⋊D3—54no—
116C2×C3⋊D3—52no—
117C32×C4—52no—
118C3⋊Dic3C22×D512yes—
119C3×Dic3—54no—
120C3×Dic3C22×D514yes—
121C22×Q8—451noSylow
122C2×C3×C5—21no—
123C2×C3×C5—22no—
124C2×C3×C5D3×Q814yescomplemented
125C2×C3×C5C23×D312yes—
126D15—38no—
127D15—64no—
128C22×D3—152no—
129C22×D3—301no—
130C3×Q8—158no—
131C2×C3×C4—32no—
132C2×C3×C4—52no—
133C2×C3×C4—101no—
134C2×C3×C4—152no—
135C2×Dic3—32no—
136C2×Dic3—52no—
137C2×Dic3—61no—
138C2×Dic3D3×D512yes—
139C4×D3—158no—
140C4×D3—158no—
141C4×D3—158no—
142C4×D3—304no—
143Dic6—38no—
144Dic6—58no—
145Dic6—158no—
146C22×C5C2×D3211yescharacteristic
147C2×D5—92no—
148C2×D5—94no—
149C4×C5—34no—
150C4×C5—92no—
151Dic5—34no—
152Dic5C2×D3212yes—
153C2×C32Q8×D512yescomplemented
154C2×C32C23×D511yescharacteristic
155C3⋊D3—54no—
156C2×Q8—91no—
157C2×Q8—152no—
158C2×Q8—451no—
159C2×Q8—458no—
160C22×C4—452no—
161C22×C4—451no—
162C3×C5—21no—
163C3×C5C2×D3×Q812yescomplemented
164C22×C3—21no—
165C22×C3C2×D3×D512yes—
166C2×D3—158no—
167C2×D3—154no—
168C2×D3—302no—
169C2×D3—304no—
170C3×C4—34no—
171C3×C4—54no—
172C3×C4—102no—
173C3×C4—154no—
174Dic3—34no—
175Dic3—54no—
176Dic3—62no—
177Dic3C2×D3×D514yes—
178C2×C5#379712yescomplemented
179C2×C5C22×D3211yescharacteristic
180D5—94no—
181C32C2×Q8×D511yescharacteristic, complemented, Sylow
182C23—451no—
183Q8—94no—
184Q8—158no—
185Q8—454no—
186C2×C4—32no—
187C2×C4—51no—
188C2×C4—91no—
189C2×C4—152no—
190C2×C4—458no—
191C2×C4—454no—
192C2×C3—22no—
193C2×C3—21no—
194C2×C3D15⋊Q814yescomplemented
195C2×C3C22×D3×D512yes—
196D3—158no—
197D3—304no—
198C5C2×#379711yescharacteristic, complemented, Sylow
199C22—454no—
200C22—452no—
201C22D32×D511yescharacteristic
202C4—34no—
203C4—52no—
204C4—92no—
205C4—154no—
206C3—21no—
207C3C2×D15⋊Q812yescomplemented
208C2—454no—
209C2#1062404012yesdirect product factor
210C2C2×D32×D511yescharacteristic
subgroupG/H
center, hypercenterC22D32×D5
commutator, cosocleC2×C32×C5C24
FrattiniC2C2×D32×D5
Fitting, socleC22×C32×C5C23
prime radicalC22×C3⋊D15C22
hypocenterC32×C5C22×Q8
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#67158C2semidirect
3. C2×C5×#627C2semidirect
5. C2×C3×#1204C2semidirect
6. #10624040C2direct (N × H)
13. #67158C22semidirect
15. C5×#627C22semidirect
17. C3×#1204C22semidirect
23. C2×#1204D3semidirect
29. C2×C3⋊D15Q8semidirect
39. C2×#627D5semidirect
56. #1204C2×D3semidirect
61. C2×C32×C5C2×Q8semidirect
63. C3⋊D15C2×Q8semidirect
78. #627C2×D5semidirect
103. C32×C5C22×Q8semidirect
124. C2×C3×C5D3×Q8semidirect
153. C2×C32Q8×D5semidirect
163. C3×C5C2×D3×Q8semidirect
178. C2×C5#3797semidirect
181. C32C2×Q8×D5semidirect
194. C2×C3D15⋊Q8semidirect
198. C5C2×#3797semidirect
207. C3C2×D15⋊Q8semidirect
209. C2#10624040direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#671582
C2×#671492
C2×C5×#6272
C2×#671372
C2×C3×#12042
#106240402
C2×D15⋊Q83
C2×#37975